pp d 2 * Hz Hz 3 10 db Wind-induced noise, Noise reduction, Microphone array, Beamforming 1

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1 pp d 2 * Hz Hz 3 10 db Wind-induced noise, Noise reduction, Microphone array, Beamforming PSS [1] [2 4] 2 Wind-induced noise reduction using a small twochannel microphone array, by Naoto Sakata, Tetsuro Murakami, Hirofumi Nakajima and Kazuhiro Nakadai Naoto Sakata@clarion. co.jp SN 1.2 [5] [6] 2 Crosswind Downwind 1 exp( 7x) exp( 3.2x) x λ d x = d/λ λ = v/f v m/s f [7] [2] 2 [3] 3 [4] [2 4]

2 cm Crosswind Downwind d mm v m/s IC khz 30 s 3 TCM (a) 4mm AV-LEADER TCM-370 2(b) L R L R AV-LEADER TCM NEOVE FTS30-T12 IC TASCAM DR-05 CELESTRON CE γ(a l (ω),b l (ω)) γ(a l (ω),b l (ω))= A l (ω)b l(ω) A l (ω) 2 B l (ω) 2 (1) A l (ω) B l (ω) ω l = 1, 2,...,L A l (ω) A l (ω) l = L l=1 A l(ω)/la l (ω) A l (ω) γ c (ω) γ c (ω) =γ(x 1,l (ω),x 2,l (ω)) (2) X 1,l (ω) X 2,l (ω) 1, 2

3 L 2 R X 1,l (ω) X 1,l (ω) = N 1 n=0 x 1 (n + Sl)w(n)e jωn/f s (3) j w(n) x 1 (n) 1 n N FFT S f s X 2,l (ω) x 2 (n) N =2 12 S = N/2 w(n) γ a (ω) γ a (ω) =γ(g( X 1,l (ω) ),G( X 2,l (ω) )) (4) G(A s,l (ω)) A s,l (ω) l 0 G(A s,l (ω)) = A s,l (ω) A s,l (ω) s γ p (ω) γ p (ω) =γ(g( X 1,l (ω) 2 ),G( X 2,l (ω) 2 )) (5) v =2.2m/s Downwind d =10mm 3 γ c (ω) 125 Hz Hz PSS 1 8kHz 6 v =2.2m/s Downwind 10 mm v =2.2m/s d =10mm Downwind [6] 8 d =10mm Downwind

4 n h(n) q(n) k(n) (6) 9 Y (ω) =X(ω)H(ω)+Q(ω)K(ω) (7) 1 4kHz v =1.1m/s 9 v =2.2m/s d =10mm Downwind Hz 50 Hz Hz x(n) y(n) y(n) =x(n) h(n)+q(n) k(n) (6) (6) (7) 4.2 L R l(n) r(n) l m (n) r m (n) l m (n) r m (n) w(n) FFT L m (ω) R m (ω) L m (ω) L m (ω) = FFT{l m (n)w(n),n} (8) N FFT{x(n),N} x(n) N FFT R m (ω) L m (ω) L m (ω) R m (ω) G L (ω) G R (ω) Z m (ω) Z m (ω) =G L (ω)l m (ω)+g R (ω)r m (ω) (9) G L (ω) G R (ω) G L (ω) G R (ω) IFFT G L (ω) G R (ω) g L (ω) g R (ω) g L (n) = IFFT {G L (ω),n} (10) g R (n) = IFFT {G R (ω),n} (11) IFFT {X(ω),N} X(ω) N g L (n) g R (n) l(n) r(n) z(n) =g L (n) l(n)+g R (n) r(n) (12)

5 2 743 z(n) 12 G L (ω) =1 G R (ω) LS-BF SS-BF LS-BF G L (ω) =1 0 G R (ω) L m (ω) R m (ω) L(ω) R(ω) (7) L(ω) =Q(ω)K L (ω) (13) R(ω) =Q(ω)K R (ω) (14) K L (ω) K R (ω) L R (9) (13) (14) Z(ω) Z(ω) =1 Q(ω)K L (ω)+g R (ω)q(ω)k R (ω) (15) Z(ω) =0 G R (ω) G R (ω) G R (ω) = K L(ω) (16) K R (ω) 4.4 SS-BF L R K L (ω) K R (ω) H L (ω) H R (ω) L(ω) R(ω) L(ω) R(ω) (7) L(ω) =X(ω)H L (ω)+q(ω)k L (ω) (17) R(ω) =X(ω)H R (ω)+q(ω)k R (ω) (18) (9) Z(ω) Z(ω) = X(ω)(G L (ω)h L (ω)+g R (ω)h R (ω)) +Q(ω)(G L (ω)k L (ω)+g R (ω)k R (ω)) (19) L X(ω)H L (ω) R Q(ω)K R (ω) Z(ω) ( = X(ω)H L (ω) G L (ω)+g R (ω) H ) R(ω) H L (ω) ( +Q(ω)K R (ω) G L (ω) K ) L(ω) K R (ω) + G R(ω) (20) 0 G L (ω) G R (ω) (20) G L (ω) G R (ω) G L (ω)+g R (ω) H R(ω) H L (ω) = 1 (21) G L (ω) K L(ω) K R (ω) + G R(ω) = 0 (22) H R (ω)/h L (ω)=h LR (ω) K L (ω)/k R (ω)=k RL (ω) (21) (22) 1 G L (ω) = K RL (ω)h LR (ω) 1 K RL (ω) G R (ω) = K RL (ω)h LR (ω) 1 (23) (24) H LR (ω) L R K RL (ω) R L 4.5 LS-BF SS-BF PSS [1] SN [8] D2 DAS-KJ191 AD/DA M-Audio Fast Track Pro PC Lenovo ThinkPad L BOSE 101-MM 12 YAMAHA MX-1 RWC [9] No khz

6 K RL (ω) =e jωt u (26) cm Downwind d mm v m/s 44.1 khz 10 s BOSE 101-MM H LR (ω) K RL(ω) H LR (ω) K RL(ω) H LR (ω) =e jωt s (25) t s L R t u R L t s 340 m/s d t u 2 φ(ω) φ(ω) φ(ω) =unwrap{arg {γ c (ω)}} (27) arg{} unwrap{} ˆτ J(τ) τ J(τ) τ φ(ω) ( ωτ) 2 ˆτ J(τ) P J(τ) = φ(ω p ) ( ω p τ) 2 (28) p=1 ω p p P φ(ω) ( ωτ) φ(ω) ( ωτ) ˆτ ˆτ = ω + φ (29) ω 0 ω P φ ω (φ = φ(ω)) ω + ω L R H LR (ω) TSP Time-Stretched Pulse TSP 10 H L (ω) H R (ω) TSP H L (ω) H R (ω) H LR (ω) H R (ω)h L (ω) H LR (ω) = H L (ω) 2 +max ( H L (ω) 2) r h (30) r h

7 K RL (ω) R L L m (ω) R m (ω) L m (ω) R m (ω) ω L ω R ω ω R L K RL (ω) L ω L ω = K RL (ω)r ω (31) R ω R + ω K RL (ω) K RL (ω) =R + ω L ω (32) K RL (ω) K RL (ω)r m (ω) L m (ω) (23) (24) SS-BF K RL (ω α )H LR (ω α )=1 ω = ω α SS-BF d(ω) G L (ω) = d(ω) 2 +max ( d(ω) 2) (33) r g G R (ω) = K RL (ω)d(ω) d(ω) 2 +max ( d(ω) 2) r g (34) r g d(ω) d(ω) =H LR (ω)k RL (ω) 1 (35) SN x(n) P x (ω) x(n) x m (n) (8) X m (ω) P x (ω) = 1 M X m (ω) 2 (36) M m=1 M f 1 f 2 SN f 1 f 2 ω p p 1 p 2 ω p1 =2πf 1 ω p2 =2πf 2 SNR(p 1,p 2 ) =10log 10 ( p2 p=p 1 P s (ω p ) p2 p=p 1 {P s+n (ω p ) P s (ω p )} ) (37) P s (ω) P s+n (ω) 37 p2 p=p 1 {P s+n (ω p ) P s (ω p )} 0 SNR(p 1,p 2 )=0 [8] κ ratio κ ori κ proc κ κ = M P Cmp 4 m=1 p=1 MP ( M P Cmp 2 m=1 p=1 MP ) 2 (38) C mp m p M P (8) 2 (38) κ ori κ proc κ ratio κ ratio = κ proc κ ori (39) κ ratio κ ori κ proc m/s 2,048 1,024 FFT PSS r h =10 4 r g =10 2 Downwind t s =0 t u = Crosswind t s = t u =0 SN 0 22,050 Hz

8 Hz ,000 Hz 3 PSS 20 PSS Cr Crosswind Original L PSS 500 Hz 8dB 1,000 Hz Original PSS LS-BF Original SS-BF 500 Hz 15 db 1,000 8,000 Hz 14 Dw Downwind PSS Cr LS-BF SS-BF 50 1,000 Hz Original 5dB 3 SN SN LS-BF SS-BF PSS SN LS-BF SN SS-BF Cr 13 db SN PSS Hz 6dB Cr SS-BF SN PSS 6dB Cr Dw 3 SN LS-BF SS-BF PSS Cr 0 22,050 Hz 2.7 db 12.9 db 6.4 db Cr Hz 2.8 db 13.3 db 6.5 db Cr ,000 Hz 2.5 db 3.3 db 1.8 db Dw 0 22,050 Hz 0.8 db 1.6 db 7.7 db Dw Hz 0.8 db 1.5 db 7.8 db Dw ,000 Hz 1.8 db 1.1 db 1.8 db 15 Cr Cr 250 1,000 Hz LS-BF SS-BF LS-BF 125 Hz 5dB 2,000 4,000 Hz 10 db SS-BF 250 Hz 3dB 16 Dw

9 LS-BF SS-BF PSS Cr Cr Dw Dw Dw 4 SN LS-BF SS-BF PSS Cr 0 22,050 Hz 2.9 db 2.3 db 6.4 db Cr Hz 3.1 db 2.2 db 6.5 db Cr ,000 Hz 0.3 db 0.2 db 1.8 db Dw 0 22,050 Hz 2.2 db 1.0 db 7.7 db Dw Hz 2.3 db 1.1 db 7.8 db Dw ,000 Hz 0.4 db 1.4 db 1.8 db 17 LS-BF 250 1,000 Hz Cr 125 Hz 5dB 2,000 4,000 Hz 10 db SS-BF 62.5 Hz 3dB Hz 3dB 4 SN 0 22,050 Hz Hz Cr Dw LS-BF 3dB SS-BF SN 2dB ,000 Hz SN Dw LS-BF SN ,000 Hz SS-BF 0 22,050 Hz Hz SS-BF SN 2dB ,000 Hz SS-BF SN 1.5 db PSS LS-BF SS-BF 5 PSS Cr 2.09 Dw 4.38 LS-BF SS-BF Cr Dw PSS LS-BF SS-BF PSS Dw v =2.6m/s SN 30 db PSS 19 SS-BF 17 PSS SS-BF 1.06 PSS 3.47 SS-BF

10 PSS [ 5 ] R. Raspet, J. Webster and K. Dillion, Framework for wind noise studies, J. Acoust. Soc. Am., 119, (2006). [ 6 ] F. Shields, Low-frequency wind noise correlation in microphone arrays, J. Acoust. Soc. Am., 117, (2005). [ 7 ] D. Herman, Wind noise rejection apparatus, U. S. Patent, US 8,391,529 B2 (2013). [ 8 ] Y. Uemura, Y. Takahashi, H. Saruwatari, K. Shikano and K. Kondo, Automatic optimization scheme of spectral subtraction based on musical noise assessment via higher-order statistics, Proc. Int. Workshop Acoustic Echo and Noise Control (2008). [ 9 ] M. Goto, H. Hashiguchi, T. Nishimura and R. Oka, RWC music database: Popular, classical, and jazz music databases, Proc. 3rd Int. Conf. Music Information Retrieval (ISMIR 2002 ), pp (2002) SS-BF Hz Hz 3 10 db PSS [ 1 ] S. F. Boll, Suppression of acoustic noise in speech using spectral subtraction, IEEE Trans. Acoust. Speech Signal Process., 27, (1979). [ 2 ] M. Yoshida and T. Oku, Wind noise reduction device, U. S. Patent, US 8,428,275 B2 (2013). [ 3 ] Y. Chung, Rejection of flow noise using a coherence function method, J. Acoust. Soc. Am., 62, (1977). [ 4 ] K. Kumatani, B. Raj, R. Singh and J. McDonough, Microphone array post-filter based on spatially-correlated noise, Proc. Interspeech 2012 (2012) NTT NTT JST ERATO IEEE

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